It's dirt easy to be admitted into practically any one of the LSE's external programmes. Whilst the administration insists that graduates of the programme are held in the same regard as internal students, industry professionals certainly don't believe likewise -- and that's what really matters. The EP is a cash cow for the LSE, which runs it simply to fund scholarships, subsidise home students, compensate professors, and so on. I'm probably going to take some flak for this, but my opinion is based on informed research and exchanges with existing students both on the internal and external programmes, university staff, and employers.
If you're in London, why don't you apply as a student of the internal 3-year programme? As a home student, you also pay remarkably low fees.